Symmetric Unique Neighbor Expanders and Good LDPC Codes

摘要

An infinite family of bounded-degree 'unique-neighbor' expanders wasconstructed explicitly by Alon and Capalbo (2002). We present an infinitefamily F of bounded-degree unique-neighbor expanders with the additionalproperty that every graph in the family F is a Cayley graph. This answers aquestion raised by Tali Kaufman. Using the same methods, we show that thesymmetric LDPC codes constructed by Kaufman and Lubotzky (2012) are in factsymmetric under a simply transitive group action on coordinates.